What percent of the volume of a 10×10×10 box can be filled with 4×4×4 wooden cubes? Express your answer as a decimal to the nearest tenth.
2*2*2
You can not line 3 up in any direction
that is 8 units long by 8 wide by 8 high = 512 units cubed
out of 10 *10*10 = 1000 units cubed
so
percent = 100 (512/1000) = 51.2 %
To find the percentage of the volume that can be filled with the wooden cubes, we need to determine the volume of the wooden cubes and the volume of the larger box.
Volume of the wooden cube = length × width × height = 4 × 4 × 4 = 64 cubic units
Volume of the larger box = length × width × height = 10 × 10 × 10 = 1000 cubic units
Now, to find the percentage filled, we divide the volume of the wooden cubes by the volume of the larger box, and then multiply by 100 to convert it to a percentage.
Percentage filled = (Volume of wooden cubes / Volume of larger box) * 100
Percentage filled = (64 / 1000) * 100
Percentage filled = 0.064 * 100 = 6.4%
So, approximately 6.4% of the volume of the 10×10×10 box can be filled with the 4×4×4 wooden cubes.